A criterion for checking if a convex set belongs to the union of a finite number of convex sets

D. G. Pivovarchuk

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

Abstract: A necessary and sufficient condition for the inclusion of a convex compact set in the union of a finite number of convex sets is proved. This condition obtained using the convex analysis techniques is a condition on the maximin of a given function. Using the dynamic programming, checking this condition is reduced to evaluating a set of functions and checking a condition for their values. The reduced form of the criterion is more convenient from the computational point of view.

Key words: convex sets, union of sets, convex analysis, dynamic programming, optimal control.

UDC: 519.658

Received: 08.12.2008

 English version: Computational Mathematics and Mathematical Physics, 2009, 49:9, 1499–1506

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